Transcript APStatsChap1

David S. Moore
The Basic Practice of Statistics
Fourth Edition
Chapter 1:
Picturing Distributions with Graphs
Copyright © 2007 by W. H. Freeman & Company
Statistics – The study of how to collect, organize, analyze and
interpret numerical information from data for the purpose of
making decisions.
Important aspects of any graphical representation are
Shape, Center, Spread.
Graphs such as bar charts or pie charts help
display the distribution of a variable
Dot plots
•Does not have to begin at zero.
•Should cover the range of values.
Histogram
Classes
15<
% adults with
bachelors
degree
< 20
20<
“
<25
25<
“
<30
30<
“
<35
35<
“
<40
40<
“
<45
•Groups data into classes.
•You can choose classes but must do so carefully.
symmetric
Skewed right
•Used for small data sets.
•Presents more detail.
•All data is displayed
Measurements of Center
The mean is nonresistant (changed) to extreme observations
or outliers; while the median is resistant (not changed).
Mean and median
are the same
Mean
Median
Measuring Spread
•Measuring center alone can be misleading.
•Often the spread or variability of the data is very important.
Range
The difference between the largest and smallest
observations.
Example:
odd # of Observations
4 6 7 8 12 17 20 31 38 40 52
Q1
Q3
M
even # of Observations
4 6 7 8 12 17 20 31 38 40
Q1
14.5
Q3
Properties of Standard deviation
• measures spread about the mean. Should only be used
when the mean is the measure of center.
• s = 0; only when there is no spread, all observations are
exactly the same.
• s is large; values are very spread out.
• s is small; values are clustered close to the mean.
• s is nonresistant likex (mean); strongly influenced by
extreme observations or outliers.